Adaptive Posterior Mode Estimation of a Sparse Sequence for Model Selection

Sylvain Sardy

Scandinavian Journal of Statistics, 2009, vol. 36, issue 4, 577-601

Abstract: Abstract. For the problem of estimating a sparse sequence of coefficients of a parametric or non‐parametric generalized linear model, posterior mode estimation with a Subbotin(λ,ν) prior achieves thresholding and therefore model selection when ν ∈ [0,1] for a class of likelihood functions. The proposed estimator also offers a continuum between the (forward/backward) best subset estimator (ν = 0), its approximate convexification called lasso (ν = 1) and ridge regression (ν = 2). Rather than fixing ν, selecting the two hyperparameters λ and ν adds flexibility for a better fit, provided both are well selected from the data. Considering first the canonical Gaussian model, we generalize the Stein unbiased risk estimate, SURE(λ,ν), to the situation where the thresholding function is not almost differentiable (i.e. ν 1). We then propose a more general selection of λ and ν by deriving an information criterion that can be employed for instance for the lasso or wavelet smoothing. We investigate some asymptotic properties in parametric and non‐parametric settings. Simulations and applications to real data show excellent performance.

Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://doi.org/10.1111/j.1467-9469.2009.00654.x

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:36:y:2009:i:4:p:577-601

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0303-6898

Access Statistics for this article

Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist

More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association
Bibliographic data for series maintained by Wiley Content Delivery ().